It could be Estriol (E3) and Estetrol (E4) which are present during pregnancy. Estradiol (E2) has to be low during that time. Still its progesterone that increases prolactin.

https://en.wikipedia.org/wiki/Estriol
https://en.wikipedia.org/wiki/Estetrol

During pregnancy, high circulating concentrations of estrogen increase prolactin levels by 10- to 20-fold.

Ok.

Prolactin reduces FSH and LH, which stops menstruation, perhaps not estrogens themselves. I think FSH and LH increases are associated with estrogen, so being not a direct effect of prolactin to estrogen, so previously I made a jump from what may have been indirectly affected.

Low levels of SHBG (and high levels of androgens) are associated with PCOS, and lack of menstruation. http://labtestsonline.org/understanding/analytes/shbg/tab/test